Does watching TV series in which the name of Allah is pronounced increase sin, and does skipping the scene in which the name of Allah was pronounced remove the sin?

The mere utterance of God's name by actors in TV series is not inherently forbidden if the utterance is befitting of Allah the Almighty. The ruling on whether watching a series is permissible or forbidden depends on its content. If it includes religiously prohibited elements, then watching it is forbidden, regardless of whether God's name is uttered or not. If it is free from prohibitions, then there is no harm in watching it.